{"id":110682,"date":"2026-09-29T07:51:10","date_gmt":"2026-09-28T23:51:10","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/110682.html"},"modified":"2026-09-29T07:51:10","modified_gmt":"2026-09-28T23:51:10","slug":"237%e3%80%81%e3%80%90ai%e3%80%91%e3%80%90%e6%a8%a1%e5%9e%8b%e9%83%a8%e7%bd%b2%e3%80%91%e5%9f%ba%e5%ba%a7%e6%a8%a1%e5%9e%8b%e7%a0%94%e7%a9%b6%ef%bc%9a%e5%8f%8d%e5%90%91%e4%bc%a0%e6%92%ad","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/110682.html","title":{"rendered":"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad"},"content":{"rendered":"<p>\u3010\u58f0\u660e\u3011\u672c\u535a\u5ba2\u6240\u6709\u5185\u5bb9\u5747\u4e3a\u4e2a\u4eba\u4e1a\u4f59\u65f6\u95f4\u521b\u4f5c&#xff0c;\u6240\u8ff0\u6280\u672f\u6848\u4f8b\u5747\u6765\u81ea\u516c\u5f00\u5f00\u6e90\u9879\u76ee&#xff08;\u5982Github&#xff0c;Apache\u57fa\u91d1\u4f1a&#xff09;&#xff0c;\u4e0d\u6d89\u53ca\u4efb\u4f55\u4f01\u4e1a\u673a\u5bc6\u6216\u672a\u516c\u5f00\u6280\u672f&#xff0c;\u5982\u6709\u4fb5\u6743\u8bf7\u8054\u7cfb\u5220\u9664<\/p>\n<h2>\u6807\u9898<\/h2>\n<p>237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u53cd\u5411\u4f20\u64ad<\/p>\n<h2>\u80cc\u666f<\/h2>\n<p>\u4e0a\u7bc7 blog \u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u786c\u6807\u7b7e\u4e0e\u8f6f\u6807\u7b7e \u628a\u8bad\u7ec3\u76ee\u6807\u8bb2\u6e05\u4e86&#xff1a;\u771f\u5b9e\u6807\u7b7e\u9ed8\u8ba4\u662f\u786c\u6807\u7b7e&#xff08;one-hot&#xff09;&#xff0c;\u4f46\u6a21\u578b\u8f93\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u4e00\u76f4\u662f\u8f6f\u7684&#xff1b;\u4e3a\u4e86\u7f13\u89e3\u8fc7\u5ea6\u81ea\u4fe1\u3001\u7ed9\u5176\u4ed6 token \u4e00\u70b9\u673a\u4f1a&#xff0c;\u53ef\u4ee5\u7528\u6807\u7b7e\u5e73\u6ed1\u6216\u77e5\u8bc6\u84b8\u998f\u628a\u76ee\u6807\u6362\u6210\u8f6f\u6807\u7b7e&#xff0c;\u63a8\u7406\u65f6\u8fd8\u80fd\u9760\u6e29\u5ea6\u4e0e top-k\/top-p \u91c7\u6837\u8c03\u8282\u591a\u6837\u6027\u3002\u65e0\u8bba\u76ee\u6807\u7528\u786c\u6807\u7b7e\u8fd8\u662f\u8f6f\u6807\u7b7e&#xff0c;\u6700\u540e\u90fd\u8981\u7b97\u4e00\u4e2a\u635f\u5931&#xff08;\u4ea4\u53c9\u71b5&#xff09;&#xff0c;\u518d\u9762\u5bf9\u540c\u4e00\u4e2a\u95ee\u9898&#xff1a;\u77e5\u9053&#034;\u9519\u4e86\u591a\u5c11&#034;\u4e4b\u540e&#xff0c;\u600e\u4e48\u77e5\u9053\u6bcf\u4e2a\u53c2\u6570\u8be5\u6539\u591a\u5c11&#xff1f; \u8fd9\u6b63\u662f\u672c\u7bc7\u8981\u8bb2\u7684\u53cd\u5411\u4f20\u64ad\u3002<\/p>\n<h2>\u6a21\u578b\u90e8\u7f72<\/h2>\n<p>\u8bad\u7ec3\u5faa\u73af\u91cc&#xff0c;loss.backward() \u53ea\u5360\u4e00\u884c&#xff0c;\u4f46\u5b83\u627f\u62c5\u4e86\u6574\u4e2a\u8bad\u7ec3\u7684&#034;\u5f52\u56e0&#034;\u5de5\u4f5c&#xff1a;\u628a\u6700\u540e\u7684\u8bef\u5dee&#xff0c;\u6309\u8d21\u732e\u5927\u5c0f\u5206\u644a\u5230\u6210\u5343\u4e0a\u4e07\u4e2a\u53c2\u6570\u4e0a\u3002\u8fd9\u7bc7\u628a backward() \u62c6\u5f00&#xff0c;\u4ece\u94fe\u5f0f\u6cd5\u5219\u8bb2\u5230\u4ee3\u7801\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; \u4ece\u94fe\u5f0f\u6cd5\u5219\u8bf4\u8d77<\/p>\n<p>\u53cd\u5411\u4f20\u64ad\u7684\u6570\u5b66\u5185\u6838\u662f\u94fe\u5f0f\u6cd5\u5219&#xff08;chain rule&#xff09;&#xff1a;\u590d\u5408\u51fd\u6570\u6c42\u5bfc&#xff0c;\u5916\u5c42\u5bfc\u6570\u4e58\u4ee5\u5185\u5c42\u5bfc\u6570\u3002\u4e00\u4e2a\u6700\u7b80\u5355\u7684\u4e24\u5c42\u51fd\u6570&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         y<\/p>\n<p>         &#061;<\/p>\n<p>         w<\/p>\n<p>         x<\/p>\n<p>         &#043;<\/p>\n<p>         b<\/p>\n<p>         ,<\/p>\n<p>         L<\/p>\n<p>         &#061;<\/p>\n<p>         (<\/p>\n<p>         y<\/p>\n<p>         \u2212<\/p>\n<p>         t<\/p>\n<p>          )<\/p>\n<p>          2<\/p>\n<p>        y &#061; wx &#043; b,\\\\qquad L &#061; (y-t)^2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u60f3\u6c42\u635f\u5931\u5bf9\u53c2\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>       w<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u7684\u5bfc\u6570&#xff0c;\u5c31\u4e00\u5c42\u5c42\u5f80\u56de\u4e58&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u2202<\/p>\n<p>           L<\/p>\n<p>           \u2202<\/p>\n<p>           w<\/p>\n<p>         &#061;<\/p>\n<p>           \u2202<\/p>\n<p>           L<\/p>\n<p>           \u2202<\/p>\n<p>           y<\/p>\n<p>         \u22c5<\/p>\n<p>           \u2202<\/p>\n<p>           y<\/p>\n<p>           \u2202<\/p>\n<p>           w<\/p>\n<p>         &#061;<\/p>\n<p>         2<\/p>\n<p>         (<\/p>\n<p>         y<\/p>\n<p>         \u2212<\/p>\n<p>         t<\/p>\n<p>         )<\/p>\n<p>         \u22c5<\/p>\n<p>         x<\/p>\n<p>        \\\\frac{\\\\partial L}{\\\\partial w} &#061; \\\\frac{\\\\partial L}{\\\\partial y}\\\\cdot\\\\frac{\\\\partial y}{\\\\partial w} &#061; 2(y-t)\\\\cdot x<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2519em;vertical-align: -0.8804em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260928235107-6abafd6bcadad.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 2 \u5c55\u793a\u4e86\u8fd9\u6761\u94fe&#xff1a;\u5148\u7b97 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        L<\/p>\n<p>       L<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u7684\u654f\u611f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>        (<\/p>\n<p>        y<\/p>\n<p>        \u2212<\/p>\n<p>        t<\/p>\n<p>        )<\/p>\n<p>       2(y-t)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u518d\u4e58 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>       w<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u7684\u654f\u611f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>\u3002&#034;\u654f\u611f\u5ea6&#034;\u5c31\u662f\u5bfc\u6570\u7684\u7269\u7406\u542b\u4e49\u2014\u2014<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>       w<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u52a8\u4e00\u70b9\u70b9&#xff0c;\u635f\u5931\u4f1a\u8ddf\u7740\u52a8\u591a\u5c11\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; \u8ba1\u7b97\u56fe&#xff1a;\u524d\u5411\u7b97\u6570\u503c&#xff0c;\u53cd\u5411\u7b97\u68af\u5ea6<\/p>\n<p>\u628a\u4e0a\u9762\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>        \u2192<\/p>\n<p>        y<\/p>\n<p>        \u2192<\/p>\n<p>        L<\/p>\n<p>       x \\\\to y \\\\to L<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u6bcf\u4e00\u6b65\u90fd\u770b\u6210\u4e00\u4e2a\u8282\u70b9&#xff0c;\u5c31\u5f97\u5230\u4e00\u5f20\u8ba1\u7b97\u56fe&#xff08;computational graph&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u524d\u5411&#xff1a;\u4ece\u8f93\u5165\u5f80\u8f93\u51fa&#xff0c;\u8fb9\u8d70\u8fb9\u7b97\u6570\u503c&#xff0c;\u5e76\u628a\u6bcf\u4e00\u6b65\u7684\u4e2d\u95f4\u7ed3\u679c\u8bb0\u4e0b\u6765&#xff1b;<\/li>\n<li>\u53cd\u5411&#xff1a;\u4ece\u635f\u5931\u8282\u70b9\u51fa\u53d1\u5f80\u56de\u8d70&#xff0c;\u6bcf\u4e2a\u8282\u70b9\u7528&#034;\u4e0a\u6e38\u4f20\u6765\u7684\u68af\u5ea6 \u00d7 \u672c\u8282\u70b9\u5c40\u90e8\u5bfc\u6570&#034;\u7b97\u51fa\u5bf9\u6d41\u7ecf\u53d8\u91cf\u7684\u68af\u5ea6\u3002<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260928235108-6abafd6c18c6e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56e0\u4e3a\u53cd\u5411\u8d70\u7684\u662f\u540c\u4e00\u6761\u56fe\u7684\u9006\u5e8f&#xff0c;\u6240\u4ee5\u6574\u4f53\u4ee3\u4ef7\u53ea\u6bd4\u524d\u5411\u591a\u4e00\u4e2a\u5e38\u6570\u500d&#xff08;\u7ea6 2~3 \u500d&#xff09;&#xff0c;\u8fd9\u5c31\u662f \u53cd\u5411\u6a21\u5f0f\u81ea\u52a8\u5fae\u5206&#xff08;reverse-mode automatic differentiation&#xff09;&#xff0c;\u4e5f\u662f\u5404\u6846\u67b6 autograd \u7684\u5b9e\u73b0\u65b9\u5f0f\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; \u68af\u5ea6\u5c31\u662f&#034;\u654f\u611f\u5ea6&#034;<\/p>\n<p>\u4e00\u4e2a\u53c2\u6570\u7684\u68af\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2202<\/p>\n<p>        L<\/p>\n<p>        \/<\/p>\n<p>        \u2202<\/p>\n<p>        w<\/p>\n<p>       \\\\partial L\/\\\\partial w<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mord\">\/<\/span><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u56de\u7b54\u7684\u5c31\u662f&#034;\u628a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>       w<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u8c03\u5927\u4e00\u70b9&#xff0c;\u635f\u5931\u4f1a\u53d8\u5927\u8fd8\u662f\u53d8\u5c0f\u3001\u53d8\u591a\u5c11&#034;\u3002\u5b83\u7684\u7b26\u53f7\u7ed9\u51fa\u65b9\u5411&#xff0c;\u7edd\u5bf9\u503c\u7ed9\u51fa\u5e45\u5ea6\u3002\u6574\u5f20\u7f51\u7edc\u91cc\u6210\u5343\u4e0a\u4e07\u4e2a\u53c2\u6570&#xff0c;\u53cd\u5411\u4f20\u64ad\u4f1a\u4e00\u6b21\u6027\u628a\u6bcf\u4e2a\u53c2\u6570\u7684\u68af\u5ea6\u90fd\u7b97\u51fa\u6765\u2014\u2014\u8fd9\u6b63\u662f\u5b83\u4e0d\u53ef\u66ff\u4ee3\u7684\u5730\u65b9&#xff1a;\u53c2\u6570\u91cf\u592a\u5927&#xff0c;\u9010\u4e2a\u6570\u503c\u6c42\u5bfc\u6839\u672c\u4e0d\u53ef\u884c&#xff0c;\u800c\u53cd\u5411\u4f20\u64ad\u8ba9&#034;\u6c42\u5168\u90e8\u68af\u5ea6&#034;\u548c\u524d\u5411\u540c\u9636\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; \u4e3a\u4ec0\u4e48\u4e0d\u7528\u6570\u503c\u6c42\u5bfc<\/p>\n<p>\u6700\u6734\u7d20\u7684\u60f3\u6cd5\u662f&#034;\u6270\u52a8\u4e00\u4e2a\u53c2\u6570\u3001\u770b\u635f\u5931\u53d8\u5316\u591a\u5c11&#034;&#xff0c;\u4e5f\u5c31\u662f\u6570\u503c\u5fae\u5206\u3002\u5b83\u6709\u4e24\u4e2a\u81f4\u547d\u95ee\u9898&#xff1a;<\/p>\n<li>\u4ee3\u4ef7\u592a\u9ad8&#xff1a;\u6bcf\u52a8\u4e00\u4e2a\u53c2\u6570\u90fd\u8981\u91cd\u65b0\u524d\u5411\u4e00\u6b21&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         N<\/p>\n<p>        N<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u4e2a\u53c2\u6570\u5c31\u8981 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         N<\/p>\n<p>        N<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u6b21\u524d\u5411&#xff1b;\u5343\u4ebf\u53c2\u6570\u76f4\u63a5\u4e0d\u53ef\u884c&#xff1b;<\/li>\n<li>\u7cbe\u5ea6\u5dee&#xff1a;\u7528\u6709\u9650\u5dee\u5206\u8fd1\u4f3c\u5bfc\u6570\u4f1a\u5f15\u5165\u622a\u65ad\u8bef\u5dee&#xff0c;\u8fd8\u5bb9\u6613\u88ab\u6d6e\u70b9\u8bef\u5dee\u6df9\u6ca1\u3002<\/li>\n<p>\u53cd\u5411\u4f20\u64ad\u53ea\u505a&#034;\u4e00\u6b21\u524d\u5411 &#043; \u4e00\u6b21\u53cd\u5411&#034;&#xff0c;\u5c31\u628a\u6240\u6709\u53c2\u6570\u7684\u68af\u5ea6\u90fd\u7b97\u51fa\u6765&#xff0c;\u4ee3\u4ef7\u4e0e\u524d\u5411\u540c\u9636\u2014\u2014\u8fd9\u624d\u662f\u5b83\u80fd\u8bad\u7ec3\u5927\u6a21\u578b\u7684\u6839\u672c\u539f\u56e0\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; softmax &#043; \u4ea4\u53c9\u71b5\u7684\u68af\u5ea6\u4e3a\u4ec0\u4e48\u6f02\u4eae<\/p>\n<p>\u4e0a\u7bc7\u8bb2\u5230 F.cross_entropy \u5185\u90e8\u662f softmax \u52a0\u8d1f\u5bf9\u6570\u3002\u628a\u8fd9\u4e24\u6b65\u5408\u8d77\u6765\u5bf9 logits \u6c42\u5bfc&#xff0c;\u4f1a\u5f97\u5230\u4e00\u4e2a\u6781\u5176\u7b80\u6d01\u7684\u7ed3\u679c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u2202<\/p>\n<p>           L<\/p>\n<p>           \u2202<\/p>\n<p>           z<\/p>\n<p>         &#061;<\/p>\n<p>         p<\/p>\n<p>         \u2212<\/p>\n<p>         y<\/p>\n<p>        \\\\frac{\\\\partial L}{\\\\partial z} &#061; p &#8211; y<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        p<\/p>\n<p>       p<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u662f softmax \u540e\u7684\u9884\u6d4b\u6982\u7387&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u662f\u771f\u5b9e one-hot \u6807\u7b7e\u3002\u9884\u6d4b\u5230\u54ea\u91cc\u3001\u771f\u5b9e\u5728\u54ea\u91cc&#xff0c;\u5dee\u591a\u5c11&#xff0c;\u68af\u5ea6\u5c31\u662f\u591a\u5c11\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260928235108-6abafd6c5d986.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 3 \u7528\u4e00\u4e2a 5 \u8bcd\u8868\u7684\u4f8b\u5b50\u5c55\u793a&#xff1a;\u6b63\u786e\u9879 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        p<\/p>\n<p>        \u2212<\/p>\n<p>        y<\/p>\n<p>       p-y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8d1f&#xff08;\u68af\u5ea6\u628a\u5b83\u7684\u6982\u7387\u5f80\u4e0a\u63a8&#xff09;&#xff0c;\u5176\u4f59\u9879\u4e3a\u6b63&#xff08;\u628a\u5b83\u4eec\u7684\u6982\u7387\u5f80\u4e0b\u538b&#xff09;\u3002\u8fd9\u4e5f\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u4ea4\u53c9\u71b5&#034;\u597d\u8bad\u7ec3&#034;\u2014\u2014\u68af\u5ea6\u5929\u7136\u5e26\u65b9\u5411&#xff0c;\u4e0d\u9700\u8981\u989d\u5916\u7684\u7f29\u653e\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; \u6700\u5c0f\u4f8b\u5b50&#xff1a;\u624b\u63a8\u4e00\u6b21\u66f4\u65b0<\/p>\n<p>\u7528\u6700\u524d\u9762\u90a3\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>        &#061;<\/p>\n<p>        w<\/p>\n<p>        x<\/p>\n<p>        &#043;<\/p>\n<p>        b<\/p>\n<p>        ,<\/p>\n<p>        \u00a0<\/p>\n<p>        L<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>        y<\/p>\n<p>        \u2212<\/p>\n<p>        t<\/p>\n<p>         )<\/p>\n<p>         2<\/p>\n<p>       y&#061;wx&#043;b,\\\\ L&#061;(y-t)^2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u4f8b\u5b50&#xff0c;\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>        &#061;<\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        \u00a0<\/p>\n<p>        b<\/p>\n<p>        &#061;<\/p>\n<p>        0<\/p>\n<p>        ,<\/p>\n<p>        \u00a0<\/p>\n<p>        t<\/p>\n<p>        &#061;<\/p>\n<p>        1<\/p>\n<p>       x&#061;1,\\\\ b&#061;0,\\\\ t&#061;1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5f53\u524d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>        &#061;<\/p>\n<p>        0.5<\/p>\n<p>       w&#061;0.5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span>&#xff1a;<\/p>\n<table>\n<tr>\u6b65\u9aa4\u8ba1\u7b97\u7ed3\u679c<\/tr>\n<tbody>\n<tr>\n<td align=\"left\">\u524d\u5411<\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           y<\/p>\n<p>           &#061;<\/p>\n<p>           w<\/p>\n<p>           x<\/p>\n<p>           &#043;<\/p>\n<p>           b<\/p>\n<p>          y &#061; wx&#043;b<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span><\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           0.5<\/p>\n<p>          0.5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u635f\u5931<\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           L<\/p>\n<p>           &#061;<\/p>\n<p>           (<\/p>\n<p>           y<\/p>\n<p>           \u2212<\/p>\n<p>           t<\/p>\n<p>            )<\/p>\n<p>            2<\/p>\n<p>          L&#061;(y-t)^2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           0.25<\/p>\n<p>          0.25<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.25<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u68af\u5ea6<\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>           (<\/p>\n<p>           y<\/p>\n<p>           \u2212<\/p>\n<p>           t<\/p>\n<p>           )<\/p>\n<p>           \u22c5<\/p>\n<p>           x<\/p>\n<p>          2(y-t)\\\\cdot x<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           \u2212<\/p>\n<p>           1.0<\/p>\n<p>          -1.0<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1.0<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u66f4\u65b0<\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           w<\/p>\n<p>           \u2190<\/p>\n<p>           w<\/p>\n<p>           \u2212<\/p>\n<p>           \u03b7<\/p>\n<p>           \u22c5<\/p>\n<p>           (<\/p>\n<p>           \u2212<\/p>\n<p>           1.0<\/p>\n<p>           )<\/p>\n<p>          w \\\\leftarrow w-\\\\eta\\\\cdot(-1.0)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1.0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/td>\n<td align=\"left\"><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           0.5<\/p>\n<p>           &#043;<\/p>\n<p>           \u03b7<\/p>\n<p>          0.5&#043;\\\\eta<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">0.5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u82e5\u5b66\u4e60\u7387 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u03b7<\/p>\n<p>        &#061;<\/p>\n<p>        0.1<\/p>\n<p>       \\\\eta&#061;0.1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>       w<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0.5<\/p>\n<p>       0.5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u53d8\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0.6<\/p>\n<p>       0.6<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.6<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u66f4\u63a5\u8fd1\u76ee\u6807 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u635f\u5931\u968f\u4e4b\u4e0b\u964d\u3002\u771f\u5b9e\u7f51\u7edc\u53ea\u662f\u628a\u8fd9\u4e00\u6b65\u5728\u6bcf\u5c42\u3001\u6bcf\u4e2a\u53c2\u6570\u4e0a\u91cd\u590d&#xff0c;\u5e76\u7528\u8ba1\u7b97\u56fe\u81ea\u52a8\u5b8c\u6210\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260928235108-6abafd6ca750a.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 5 \u662f\u8fd9\u4e00\u6b65\u7684\u51e0\u4f55\u76f4\u89c9&#xff1a;\u6cbf\u7740\u8d1f\u68af\u5ea6\u65b9\u5411&#xff0c;\u628a\u53c2\u6570\u5f80\u635f\u5931\u66f4\u4f4e\u7684\u5730\u65b9\u632a\u4e00\u70b9\u70b9\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; \u68af\u5ea6\u600e\u4e48\u7a7f\u8fc7\u6574\u5f20 Transformer<\/p>\n<p>\u5728\u771f\u5b9e\u6a21\u578b\u91cc&#xff0c;\u53cd\u5411\u4f20\u64ad\u8981\u4f9d\u6b21\u7a7f\u8fc7\u8f93\u51fa\u5c42 \u2192 \u6bcf\u4e00\u5c42\u7684\u5747\u65b9\u6839\u5f52\u4e00\u5316&#xff08;Root Mean Square Normalization&#xff0c;RMSNorm&#xff09;\u2192 \u524d\u9988\u7f51\u7edc&#xff08;Feed-Forward Network&#xff0c;FFN&#xff09;\u2192 \u6ce8\u610f\u529b \u2192 \u8bcd\u5d4c\u5165\u3002\u4ee5\u7b2c 231 \u7bc7\u540c\u6b3e\u7684\u5fae\u578b\u6a21\u578b\u4e3a\u4f8b&#xff0c;\u7ed3\u6784\u662f&#034;\u8bcd\u5d4c\u5165 &#043; \u82e5\u5e72 Block &#043; \u5f52\u4e00\u5316 &#043; \u8f93\u51fa\u5934&#034;&#xff1a;<\/p>\n<p>x <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>tok_emb<span class=\"token punctuation\">(<\/span>idx<span class=\"token punctuation\">)<\/span>                    <span class=\"token comment\"># \u8bcd\u5d4c\u5165<\/span><br \/>\n<span class=\"token keyword\">for<\/span> blk <span class=\"token keyword\">in<\/span> self<span class=\"token punctuation\">.<\/span>blocks<span class=\"token punctuation\">:<\/span>                  <span class=\"token comment\"># \u6bcf\u4e2a Block: RMSNorm &#043; \u6ce8\u610f\u529b &#043; RMSNorm &#043; FFN<\/span><br \/>\n    x <span class=\"token operator\">&#061;<\/span> blk<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> cos<span class=\"token punctuation\">,<\/span> sin<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">return<\/span> self<span class=\"token punctuation\">.<\/span>lm_head<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>        <span class=\"token comment\"># \u8f93\u51fa\u5934 \u2192 logits<\/span><\/p>\n<p>\u524d\u5411\u662f&#034;\u4ece\u4e0a\u5230\u4e0b&#034;\u8d70\u4e00\u904d&#xff0c;\u53cd\u5411\u5c31\u662f\u4ece lm_head \u7684\u68af\u5ea6\u5f00\u59cb&#xff0c;\u4e00\u5c42\u5c42\u5f80\u56de\u4e58&#xff0c;\u76f4\u5230\u8bcd\u5d4c\u5165\u3002\u6ce8\u610f\u529b\u91cc\u7684 matmul\u3001softmax\u3001RMSNorm\u3001SiLU \u6fc0\u6d3b&#xff0c;\u6bcf\u4e2a\u7b97\u5b50\u90fd\u6709\u5bf9\u5e94\u7684\u5c40\u90e8\u5bfc\u6570\u2014\u2014\u6846\u67b6\u5728 backward() \u65f6\u81ea\u52a8\u8c03\u7528\u5b83\u4eec\u3002<\/p>\n<hr \/>\n<p>&#x1f4ca; \u4e09\u4e2a\u63a5\u53e3&#xff1a;zero_grad \/ backward \/ step<\/p>\n<p>\u4e0a\u7bc7\u4ee3\u7801\u91cc\u7684 opt.zero_grad(); loss.backward(); opt.step()&#xff0c;\u4e09\u8005\u5206\u5de5\u660e\u786e&#xff1a;<\/p>\n<table>\n<tr>\u63a5\u53e3\u505a\u4ec0\u4e48\u5c11\u4e86\u5b83\u4f1a\u600e\u6837<\/tr>\n<tbody>\n<tr>\n<td align=\"left\">opt.zero_grad()<\/td>\n<td align=\"left\">\u628a\u4e0a\u4e00\u8f6e\u68af\u5ea6\u6e05\u96f6<\/td>\n<td align=\"left\">\u68af\u5ea6\u7d2f\u52a0&#xff0c;\u66f4\u65b0\u9519\u4e71<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">loss.backward()<\/td>\n<td align=\"left\">\u53cd\u5411\u4f20\u64ad&#xff0c;\u586b\u597d\u6bcf\u4e2a\u53c2\u6570\u7684 .grad<\/td>\n<td align=\"left\">\u6ca1\u6709\u68af\u5ea6&#xff0c;\u65e0\u6cd5\u5b66\u4e60<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">opt.step()<\/td>\n<td align=\"left\">\u7528 .grad \u66f4\u65b0\u53c2\u6570<\/td>\n<td align=\"left\">\u5149\u7b97\u4e0d\u6539&#xff0c;loss \u4e0d\u52a8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>opt \u662f\u4f18\u5316\u5668\u3002\u6700\u6734\u7d20\u7684\u66f4\u65b0\u662f\u968f\u673a\u68af\u5ea6\u4e0b\u964d&#xff08;Stochastic Gradient Descent&#xff0c;SGD&#xff09;&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        w<\/p>\n<p>        \u2190<\/p>\n<p>        w<\/p>\n<p>        \u2212<\/p>\n<p>        \u03b7<br \/>\n       \u2009<\/p>\n<p>        \u2202<\/p>\n<p>        L<\/p>\n<p>        \/<\/p>\n<p>        \u2202<\/p>\n<p>        w<\/p>\n<p>       w \\\\leftarrow w &#8211; \\\\eta\\\\,\\\\partial L\/\\\\partial w<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03b7<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mord\">\/<\/span><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span>\u3002\u5b9e\u8df5\u4e2d\u5e38\u7528 AdamW&#xff08;\u81ea\u9002\u5e94\u5b66\u4e60\u7387 &#043; \u6743\u91cd\u8870\u51cf&#xff09;&#xff0c;\u5b83\u5bf9\u4e0d\u540c\u53c2\u6570\u81ea\u52a8\u8c03\u6574\u6b65\u957f&#xff0c;\u6536\u655b\u66f4\u7a33\u2014\u2014\u5fae\u578b\u6a21\u578b\u7528\u7684\u5c31\u662f torch.optim.AdamW\u3002<\/p>\n<hr \/>\n<p>&#x1f4ca; \u4e3a\u4ec0\u4e48\u8fd8\u8981\u68af\u5ea6\u88c1\u526a\u4e0e warmup<\/p>\n<p>\u53cd\u5411\u4f20\u64ad\u628a\u5f88\u591a\u5c42\u7684\u5bfc\u6570\u8fde\u4e58&#xff0c;\u5c42\u6570\u4e00\u6df1\u5c31\u5bb9\u6613\u51fa\u4e8b&#xff1a;\u82e5\u6bcf\u5c42\u5bfc\u6570\u7ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0.5<\/p>\n<p>       0.5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8fde\u4e58\u5341\u5c42\u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         0.5<\/p>\n<p>         10<\/p>\n<p>        \u2248<\/p>\n<p>        0.001<\/p>\n<p>       0.5^{10}\\\\approx0.001<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">0.<\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.001<\/span><\/span><\/span><\/span><\/span>&#xff08;\u68af\u5ea6\u6d88\u5931&#xff09;&#xff1b;\u82e5\u6bcf\u5c42\u7ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8fde\u4e58\u5341\u5c42\u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>         10<\/p>\n<p>        &#061;<\/p>\n<p>        1024<\/p>\n<p>       2^{10}&#061;1024<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1024<\/span><\/span><\/span><\/span><\/span>&#xff08;\u68af\u5ea6\u7206\u70b8&#xff09;\u3002\u771f\u5b9e\u9884\u8bad\u7ec3\u56e0\u6b64\u52a0\u4e24\u9053\u4fdd\u9669&#xff08;\u4e0a\u7bc7\u63d0\u8fc7&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u68af\u5ea6\u88c1\u526a&#xff08;gradient clipping&#xff09;&#xff1a;\u7ed9\u68af\u5ea6\u7684\u8303\u6570\u8bbe\u4e0a\u9650&#xff0c;\u9632\u6b62\u4e00\u6b65\u8de8\u592a\u5927\u628a\u6743\u91cd\u6253\u98de&#xff1b;<\/li>\n<li>\u5b66\u4e60\u7387 warmup \u540e\u8870\u51cf&#xff1a;\u5148\u5c0f\u6b65\u70ed\u8eab\u518d\u9010\u6e10\u653e\u5927&#xff0c;\u907f\u514d\u4e00\u5f00\u59cb\u5c31\u9707\u8361\u3002<\/li>\n<\/ul>\n<p>\u8fd9\u4e9b\u5728\u5fae\u578b\u5b9e\u9a8c\u91cc\u88ab\u7701\u6389\u4e86&#xff0c;\u4f46\u653e\u5927\u5230\u5343\u4ebf\u53c2\u6570\u65f6\u662f\u5fc5\u9700\u54c1\u3002<\/p>\n<hr \/>\n<p>&#x1f9e9; \u628a\u5b83\u63a5\u56de\u9884\u8bad\u7ec3\u5faa\u73af<\/p>\n<p>\u73b0\u5728\u518d\u770b\u6574\u6761\u94fe\u8def\u5c31\u5b8c\u6574\u4e86&#xff1a;\u524d\u5411\u5f97\u5230 logits&#xff0c;\u4ea4\u53c9\u71b5\u7b97\u51fa&#034;\u9519\u4e86\u591a\u5c11&#034;&#xff0c;\u53cd\u5411\u4f20\u64ad\u628a\u8bef\u5dee\u5206\u644a\u6210\u6bcf\u4e2a\u53c2\u6570\u7684\u68af\u5ea6&#xff0c;\u4f18\u5316\u5668\u6309\u68af\u5ea6\u66f4\u65b0\u6743\u91cd&#xff0c;\u7136\u540e\u91cd\u590d\u3002\u4e0a\u7bc7\u7684 loss \u4ece 7.3883 \u4e00\u8def\u964d\u5230 0.7821&#xff0c;\u5c31\u662f\u8fd9\u4e00\u5957\u5faa\u73af\u628a\u8bed\u8a00\u7edf\u8ba1\u89c4\u5f8b\u4e00\u70b9\u70b9\u538b\u8fdb\u6743\u91cd\u7684\u8fc7\u7a0b\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260928235109-6abafd6d02fac.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u56fe 4 \u662f\u8fd9\u6761\u5faa\u73af\u7684\u603b\u89c8&#xff1a;\u524d\u5411 \u2192 \u635f\u5931 \u2192 \u53cd\u5411 \u2192 \u66f4\u65b0&#xff0c;\u91cd\u590d\u4e07\u4ebf\u6b21\u3002<\/p>\n<hr \/>\n<p>&#x1f4cc; \u4e00\u53e5\u8bdd\u8bb0\u5fc6<\/p>\n<p>\u53cd\u5411\u4f20\u64ad\u662f\u94fe\u5f0f\u6cd5\u5219\u5728\u8ba1\u7b97\u56fe\u4e0a\u7684\u53cd\u5411\u5e94\u7528&#xff1a;\u524d\u5411\u7b97\u6570\u503c&#xff0c;\u53cd\u5411\u7528&#034;\u4e0a\u6e38\u68af\u5ea6 \u00d7 \u672c\u5c42\u5c40\u90e8\u5bfc\u6570&#034;\u9010\u5c42\u6c42\u51fa\u6bcf\u4e2a\u53c2\u6570\u7684\u68af\u5ea6&#xff1b;softmax \u4e0e\u4ea4\u53c9\u71b5\u7ec4\u5408\u540e&#xff0c;\u5bf9 logits \u7684\u68af\u5ea6\u6070\u597d\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         p<\/p>\n<p>         \u2212<\/p>\n<p>         y<\/p>\n<p>        p-y<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span>&#xff1b;backward() \u586b\u597d .grad&#xff0c;\u4f18\u5316\u5668&#xff08;SGD \u6216 AdamW&#xff09;\u6309\u68af\u5ea6\u628a\u53c2\u6570\u5f80\u4f4e\u5904\u632a\u4e00\u70b9&#xff1b;\u6df1\u5c42\u7f51\u7edc\u8fd8\u8981\u9760\u68af\u5ea6\u88c1\u526a\u4e0e warmup \u4fdd\u6301\u7a33\u5b9a\u3002<\/p>\n<hr \/>\n<p>OK&#xff0c;\u672c\u7bc7\u5148\u5230\u8fd9\u91cc&#xff0c;\u5982\u6709\u7591\u95ee&#xff0c;\u6b22\u8fce\u8bc4\u8bba\u533a\u7559\u8a00\u8ba8\u8bba&#xff0c;\u795d\u5404\u4f4d\u529f\u529b\u5927\u6da8&#xff0c;\u6280\u672f\u66f4\u4e0a\u4e00\u5c42\u697c&#xff01;&#xff01;&#xff01;\u66f4\u591a\u5185\u5bb9\u89c1\u4e0b\u7bc7 blog<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3010\u58f0\u660e\u3011\u672c\u535a\u5ba2\u6240\u6709\u5185\u5bb9\u5747\u4e3a\u4e2a\u4eba\u4e1a\u4f59\u65f6\u95f4\u521b\u4f5c&#xff0c;\u6240\u8ff0\u6280\u672f\u6848\u4f8b\u5747\u6765\u81ea\u516c\u5f00\u5f00\u6e90\u9879\u76ee&#xff08;\u5982Github&#xff0c;Apache\u57fa\u91d1\u4f1a&#xff09;&#xff0c;\u4e0d\u6d89\u53ca\u4efb\u4f55\u4f01\u4e1a\u673a\u5bc6\u6216\u672a\u516c\u5f00\u6280\u672f&#xff0c;\u5982\u6709\u4fb5\u6743\u8bf7\u8054\u7cfb\u5220\u9664 \u6807\u9898<br \/>\n237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u53cd\u5411\u4f20\u64ad<br \/>\n\u80cc\u666f<br \/>\n\u4e0a\u7bc7 blog \u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u786c\u6807\u7b7e\u4e0e\u8f6f\u6807\u7b7e \u628a\u8bad\u7ec3\u76ee\u6807\u8bb2\u6e05\u4e86&#xff1a;\u771f\u5b9e\u6807\u7b7e\u9ed8\u8ba4\u662f\u786c\u6807\u7b7e&amp;#xff08<\/p>\n","protected":false},"author":2,"featured_media":110677,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[50,2094],"topic":[],"class_list":["post-110682","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-50","tag-2094"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/110682.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u3010\u58f0\u660e\u3011\u672c\u535a\u5ba2\u6240\u6709\u5185\u5bb9\u5747\u4e3a\u4e2a\u4eba\u4e1a\u4f59\u65f6\u95f4\u521b\u4f5c&#xff0c;\u6240\u8ff0\u6280\u672f\u6848\u4f8b\u5747\u6765\u81ea\u516c\u5f00\u5f00\u6e90\u9879\u76ee&#xff08;\u5982Github&#xff0c;Apache\u57fa\u91d1\u4f1a&#xff09;&#xff0c;\u4e0d\u6d89\u53ca\u4efb\u4f55\u4f01\u4e1a\u673a\u5bc6\u6216\u672a\u516c\u5f00\u6280\u672f&#xff0c;\u5982\u6709\u4fb5\u6743\u8bf7\u8054\u7cfb\u5220\u9664 \u6807\u9898 237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u53cd\u5411\u4f20\u64ad \u80cc\u666f \u4e0a\u7bc7 blog \u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u786c\u6807\u7b7e\u4e0e\u8f6f\u6807\u7b7e \u628a\u8bad\u7ec3\u76ee\u6807\u8bb2\u6e05\u4e86&#xff1a;\u771f\u5b9e\u6807\u7b7e\u9ed8\u8ba4\u662f\u786c\u6807\u7b7e&amp;#xff08\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/110682.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-09-28T23:51:10+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260928235107-6abafd6bcadad.png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/110682.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/110682.html\",\"name\":\"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-09-28T23:51:10+00:00\",\"dateModified\":\"2026-09-28T23:51:10+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/110682.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/110682.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/110682.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/110682.html","og_locale":"zh_CN","og_type":"article","og_title":"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u3010\u58f0\u660e\u3011\u672c\u535a\u5ba2\u6240\u6709\u5185\u5bb9\u5747\u4e3a\u4e2a\u4eba\u4e1a\u4f59\u65f6\u95f4\u521b\u4f5c&#xff0c;\u6240\u8ff0\u6280\u672f\u6848\u4f8b\u5747\u6765\u81ea\u516c\u5f00\u5f00\u6e90\u9879\u76ee&#xff08;\u5982Github&#xff0c;Apache\u57fa\u91d1\u4f1a&#xff09;&#xff0c;\u4e0d\u6d89\u53ca\u4efb\u4f55\u4f01\u4e1a\u673a\u5bc6\u6216\u672a\u516c\u5f00\u6280\u672f&#xff0c;\u5982\u6709\u4fb5\u6743\u8bf7\u8054\u7cfb\u5220\u9664 \u6807\u9898 237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u53cd\u5411\u4f20\u64ad \u80cc\u666f \u4e0a\u7bc7 blog \u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76&#xff1a;\u786c\u6807\u7b7e\u4e0e\u8f6f\u6807\u7b7e \u628a\u8bad\u7ec3\u76ee\u6807\u8bb2\u6e05\u4e86&#xff1a;\u771f\u5b9e\u6807\u7b7e\u9ed8\u8ba4\u662f\u786c\u6807\u7b7e&amp;#xff08","og_url":"https:\/\/www.wsisp.com\/helps\/110682.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-09-28T23:51:10+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260928235107-6abafd6bcadad.png"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"3 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/110682.html","url":"https:\/\/www.wsisp.com\/helps\/110682.html","name":"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-09-28T23:51:10+00:00","dateModified":"2026-09-28T23:51:10+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/110682.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/110682.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/110682.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"237\u3001\u3010AI\u3011\u3010\u6a21\u578b\u90e8\u7f72\u3011\u57fa\u5ea7\u6a21\u578b\u7814\u7a76\uff1a\u53cd\u5411\u4f20\u64ad"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/110682","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=110682"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/110682\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/110677"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=110682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=110682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=110682"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=110682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}